... but is it possible to marry Babette via console? I don't intend to, but the thought occurred to me that it should technically be permissible, seeing as she's well over the age of majority (even if she doesn't look it.) Has anyone tried this?

Via console, you can marry a mudcrab.

Possibilties are limitless, my fellow peculiar person :]

If you try to marry an NPC that is not set up for it, you won't have any of the dialog that comes with a spouse.

For some that may be a benefit in real life, but in the game, it would be boring.

Ha! I may try that some day on a lark.
That's only for unique NPC voices, though, right? Which I suppose Babette's would qualify as. But muteness aside, would it be possible?

No. Marriage dialogue is divided by voice type. It won't even appear if their voice doesn't have dialogue.

I suppose that you could force Babette's reference into the quest and update it with the console, but that would be an awful lot of work for no payoff.

Besides, if you have access to the console, you have access to mods. I am sure that someone somewhere will make her or some other NPCs marriable.